A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length a which will maximize the area of such a window. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of x when this occurs? largest a: cm. Determine a function A(x) which gives the area of the window in terms of the parameter x (this is the function plotted above): A(x) = cm2. Now find the exact base length x which maximizes this area: cm.

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length a which will maximize the area of such a window. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of x when this occurs? largest a: cm. Determine a function A(x) which gives the area of the window in terms of the parameter x (this is the function plotted above): A(x) = cm2. Now find the exact base length x which maximizes this area: cm.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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